Modern Machine-Shop Practice Part 187

[B] = Sum of Tensions. _T_ + _t_ Initial.

[C] = Sum of Tensions. _T_ + _t_ Working.

[D] = Sum of Tensions. _T_ + _t_ Final.

[E] = _T_ - _t_ Working.

[F] = _T_ [G] = _t_ [H] = _T_/_t_ [I] = Percentage of Slip.

[J] = Velocity of Slip in ft. per min.

[K] = Arc of contact.

[L] = Coefficient of Friction.

[M] = Remarks.

---+---+---+---+---+-----+-----+-----+----+----+----+-----+--- [A]|[B]|[C]|[D]|[E]| [F] | [G] | [H] | [I]| [J]| [K]| [L] |[M]

---+---+---+---+---+-----+-----+-----+----+----+----+-----+--- 105|100|104| | 40| 72 | 32 | 2.25| .3| 1.2|177| .263| 106| |110| | 60| 85 | 25 | 3.40| .8| 3.2|177 | .395| 107| |122| | 80| 101 | 21 | 4.81| 1.7| 6.8|176 | .511| 108| |138| |100| 119 | 19 | 6.26| 4.3|17.2|175 | .600| ---+---+---+---+---+-----+-----+-----+----+----+----+-----+--- 109|200|208| | 80| 144 | 64 | 2.25| .4| 1.6|179 | .260| 110| |212| |100| 156 | 56 | 2.81| .7| 2.8|179 | .331| 111| |216| |120| 168 | 48 | 3.50| 1 | 4 |179 | .401| 112| |220| |140| 180 | 40 | 4.50| 1.8| 7.2|178 | .484| 113| |230| |160| 195 | 35 | 5.57| 4.4|17.6|178 | .553| ---+---+---+---+---+-----+-----+-----+----+----+----+-----+--- 114|300|308| |120| 214 | 94 | 2.28| .4| 1.6|180 | .262| 116| |316| |160| 238 | 78 | 3.05| .8| 3.2|180 | .355| 118| |322| |200| 261 | 61 | 4.28| 1.6| 6.4|179 | .465| 119| |330|285|220| 275 | 55 | 5 | 2.6|10.4|179 | .516| ---+---+---+---+---+-----+-----+-----+----+----+----+-----+--- 121|400|404| |160| 282 |122 | 2.31| .7| 2.8|180 | .267| 124| |410| |220| 315 | 95 | 3.37| 1.5| 6 |180 | .387| 125| |412| |240| 326 | 86 | 3.79| 2.3| 9.2|180 | .424| 126| |414| |260| 338 | 78 | 4.33| 3.7|14.8|179 | .469| 127| |416|370|280| 348 | 68 | 5.12|10.1|40.4|179 | .523|[A]

---+---+---+---+---+-----+-----+-----+----+----+----+-----+ 128|500|516| |200|358 |158 | 2.27| .5| 2 |180 | .261| 131| |520| |260|390 |130 | 3 | 1.1| 4.4|180 | .350| 133| |525| |300|412.5|112.5| 3.67| 1.8| 7.2|180 | .414| 134| |525| |320|422.5|102.5| 4.11| 2.7|10.8|180 | .450| 135| |525|460|340|432.5| 92.5| 4.67| 5.1|20.4|180 | .490| ---+---+---+---+---+-----+-----+-----+----+----+----+-----+--- 136|100|105| | 40| 72.5| 32.5| 2.02| .2| .8|177 | .228|[B]

137| |110| | 60| 85 | 25 | 3.40| .4| 1.6|177 | .396| 138| |125| | 80|102.5| 22.5| 4.56| .6| 2.4|176 | .494| 140| |150| |120|135 | 15 | 9 | 1.8| 7.2|174 | .723| 141| |164| |140|152 | 12 |12.7 | 2.8|10.8|172 | .779| 142| |180| |160|170 | 10 |17 | 5 |20 |170 | .954| 144| |215| |200|207.5| 7.5|27.7 | 7.3|29.2|166 |1.15 | 146| |250| |240|245 | 5 |49 |10.6|42.4|158 |1.41 | 147| |270| 90|260|265 | 5 |53 |17.7|70.8|158 |1.44 | ---+---+---+---+---+-----+-----+-----+----+----+----+-----+--- 149|100|105| | 40| 72.5| 32.5| 2.02| .2| .8|177 | .228|[C]

150| |110| | 60| 85 | 25 | 3.40| .3| 1.2|177 | .396| 151| |120| | 80|100 | 20 | 5 | .4| 1.6|176 | .524| 153| |150| |120|135 | 15 | 9 | .7| 2.8|174 | .723| 155| |182| |160|171 | 11 |15.5 | 1.2| 4.8|172 | .913| 156| |202| |180|191 | 11 |17.3 | 3 |12 |172 | .950| 157| |216| |200|208 | 8 |26 | 5.8|23.2|167 |1.12 | 158| |232| |220|226 | 6 |37.3 | 7 |28 |161 |1.29 | 159| |252| |240|246 | 6 |41 | 9.8|39.2|161 |1.32 | 161| |292| |280|286 | 6 |47.7 |13.7|54.8|161 |1.37 | ---+---+---+---+---+-----+-----+-----+----+----+----+-----+---

Legend Remarks: [A] = Belt almost slipped off.

[B] = Here the belt was coated with "Sankey's Life of Leather," and run until in good working condition before noting experiments.

[C] = Three days later without any additional dressing.

A piece of belting 1 sq. in. in section and 92 ins. long was found by experiment to elongate 1/4 in. when the load was increased from 100 to 150 lbs., and only 1/8 in. when the load was increased from 450 to 500 lbs. The total elongation from 50 to 500 lbs. was 1-11/16", but this would vary with the time of suspension, and the measurements here given were taken as soon as possible after applying the loads. In a running belt the load is applied and removed alternately for short intervals of time, depending upon the length and speed of the belt, and the time for stretching would seldom be as great as that consumed in making the experiments just mentioned.

The differences between the initial and final tensions unloaded, as given in the tables, show the effect of extension or contraction during the course of the experiments made at a fixed position of the pulleys.

The percentage of elongation which a belt undergoes in pa.s.sing from its loose to its tight side, is the measure of the slip which must necessarily take place in the transmission of power. This is a direct loss, and within the a.s.sumed working strength of 500 lbs. per sq. in.

for cemented belts without lacings, experiment indicates that it should not exceed 1-1/2 or 2 per cent. When, therefore, an experiment shows less than 2 per cent. of slip, the amount may be considered as allowable and proper, and the belt may be relied upon to work continuously at the figures given.

Table III. gives the results of experiments upon a soft and pliable rawhide belt made by the Springfield Glue and Emery Co. This belt had been used by the Midvale Steel Co. for a period of seven months, at its full capacity, and was sent in its usual working condition to be tested.

It had been cleaned and dressed with castor oil at intervals of three months, and was received three weeks after the last dressing. Commencing with the light initial tension of 50 lbs. on a side, it was found impossible with the power at command to reach a limit to the pulling power of the belt, and in order to do so the experiment was made of supporting the slack side of the belt upon a board to prevent sagging.

TABLE III.

RAWHIDE BELT 4" WIDE BY 9/32" THICK AND 31 FT. LONG, WEIGHING 15 LBS.

160 R. P. M. ON 20" CAST-IRON PULLEYS.

Legend column headings: [A] = No. of Experi'nt.

[B] = Sum of Tensions. _T_ + _t_ Initial.

[C] = Sum of Tensions. _T_ + _t_ Working.

[D] = Sum of Tensions. _T_ + _t_ Final.

[E] = _T_ - _t_ Working.

[F] = _T_ [G] = _t_ [H] = _T_/_t_ [I] = Percentage of Slip.

[J] = Velocity of Slip in ft. per min.

[K] = Arc of contact.

[L] = Coefficient of Friction.

[M] = Duration of run at time of experiment.

[N] = Remarks.

---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- [A]|[B]|[C]|[D]|[E]| [F] | [G] | [H] | [I]| [J] | [K]| [L] | [M] |[N]

---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 171|100|118| | 40| 79 | 39 | 2.03| .2| .8 |177| .229| | 173| |140| | 80|110 | 30 | 3.67| .4| 1.6 |176 | .423| | 175| |168| |120|144 | 24 | 6 | .6| 2.4 |174 | .590| | 177| |202| |160|181 | 21 | 8.62| .8| 3.2 |172 | .661| | 179| |232| |200|216 | 16 | 13.5 | 1 | 4 |170 | .897| | 181| |268| |240|254 | 14 | 18.1 | 1.2| 4.8 |167 | .993| | 183| |302| |280|291 | 11 | 26.5 | 1.4| 5.6 |163 | 1.15 | | 184| |318|110|300|309 | 9 | 34.3 | 1.6| 6.4 |160 | 1.27 | | ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 185|100|150|115|140|145 | 5 | 29 | 1.6| 6.4 |180 | 1.02 | |[A]

---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+ 186|200|258| |240|249 | 9 | 27.4 | 1.2| 4.8 |180 | 1.05 | | 188| |290| |280|285 | 5 | 57 | 2.2| 8.8 |180 | 1.29 | | ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 189|300|412| |400|406 | 6 | 67.7 | 1.7| 6.8 |180 | 1.34 | | 190| |428| |420|424 | 4 |106 | 1.8| 7.2 |180 | 1.48 | | 191| |446|275|440|443 | 3 |148 | 3.3|13.2 |180 | 1.59 | | ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+ 192|400|570|360|560|565 | 5 |113 | 2 | 8 |180 | 1.47 | | ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 329|100|110| | 40| 75 | 35 | 2.14| .3| .6 |177 | .246| |[B]

330| |135| | 80|107.5| 27.5| 3.90| .6| 1.2 |175 | .446| | 331| |198| |160|179 | 19 | 9.42| 1 | 2 |171 | .751| | 332| |275| |240|257.5| 17.5| 14.7 | 1.5| 3 |169 | .911| | 334| |345| |320|232.5| 12.5| 18.6 | 2 | 4 |165 | 1.01 | | 336| |420|110|400|410 | 10 | 41 | 3.2| 6.4 |162 | 1.31 | | ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 339|200|230| |160|195 | 35 | 5.86| .8| 1.6 |176 | .576| | 340| |360| |320|340 | 20 | 17 | 1.6| 3.2 |171 | .949| | 341| |435| |400|417.5| 17.5| 23.8 | 2 | 4 |169 | 1.07 | | 342| |505| |480|492.5| 12.5| 39.4 | 2.7| 5.4 |165 | 1.28 | | 343| |590|200|560|575 | 15 | 38.3 | 5 |10 |168 | 1.24 | | ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 344|300|400| |320|360 | 40 | 9 | 1.4| 2.8 |175 | .719| | 345| |450| |400|425 | 25 | 17 | 1.7| 3.4 |173 | .938| | 346| |520| |480|500 | 20 | 25 | 2.1| 4.2 |171 | 1.08 | | 347| |600| |560|570 | 10 | 57 | 3 | 6 |162 | 1.43 | 1 min.| 348| |600|280|560|570 | 10 | 57 | 3.4| 6.8 |162 | 1.43 | 5 min.| ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 350|400|500| |400|450 | 50 | 9 | 1.6| 3.2 |176 | .715| | 352| |605| |560|577.5| 17.5| 21.3 | 2.3| 4.6 |169 | 1.04 | | 353| |680| |640|660 | 20 | 33 | 3.2| 6.4 |171 | 1.17 | 1 min.| 354| |680| |640|660 | 20 | 33 | 3.7| 7.4 |171 | 1.17 | 5 min.| 355| |680| |640|660 | 20 | 33 | 4.1| 8.2 |171 | 1.17 |10 min.| 356| |680| |640|660 | 20 | 33 | 6.1|12.2 |171 | 1.17 |15 min.|[C]

357| |600| |560|580 | 20 | 29 |10 |20 |171 | 1.13 |20 min.|[D]

358| |600| |560|580 | 20 | 29 |17.2|34.4 |171 | 1.13 |25 min.| 359| |530| |480|505 | 25 | 20.2 | 5.2|10.4 |173 | .955|30 min.| 360| |530|350|480|505 | 25 | 20.2 | 2.8| 5.6 |173 | .955|35 min.| ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 361|500|570| |400|485 | 85 | 5.71| 1.3| 2.6 |178 | .561| | 364| |700| |640|670 | 30 | 22.3 | 2.3| 4.6 |174 | 1.02 | | 365| |755| |720|637.5| 17.5| 36.4 | 3.2| 6.4 |169 | 1.22 | | 366| |820| |800|810 | 10 | 81 | 6.6|13.2 |162 | 1.55 +-------+[E]

367| |750| |720|735 | 15 | 49 | 5.1|10.2 |168 | 1.32 | 1 min.| 368| |750| |720|735 | 15 | 49 |11 |22 |168 | 1.32 | 5 min.| 369| |690| |640|665 | 25 | 26.6 |12 |24 |173 | 1.09 +-------+[F]

370| |610| |560|585 | 25 | 23.4 |14.4|28.8 |173 | 1.05 | 1 min.| 371| |610| |560|585 | 25 | 23.4 |20 |40 |173 | 1.05 | 4 min.| 372| |550| |480|515 | 35 | 14.7 | 7.4| 14.8|175 | .880| 1 min.| 373| |550|410|480|515 | 35 | 14.7 | 2.3| 4.6|175 | .880| 5 min.| ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 374|600|680| |480|580 |100 | 5.8 | 1.5| 3 |178 | .566| | 376| |755| |640|697.5| 57.5| 12.1 | 2.1| 4.2 |177 | .807| | 378| |850| |800|825 | 25 | 33 | 2.8| 5.6 |173 | 1.16 | 1 min.| 379| |850| |800|825 | 25 | 33 | 3.5| 7 |173 | 1.16 | 5 min.|[G]

380| |780| |720|750 | 30 | 25 | 8.8|17.6 |174 | 1.06 | 1 min.| 381| |680| |560|620 | 60 | 10.3 |11.2|22.4 |177 | .755| 5 min.| 382| |680| |560|620 | 60 | 10.3 | 2 | 4 |177 | .755+-------+[H]

383| |730| |640|685 | 45 | 15.2 | 2.5| 5 |176 | .886| 1 min.| 384| |730| |640|685 | 45 | 15.2 | 2.4| 4.8 |176 | .886| 5 min.| 385| |780| |720|750 | 30 | 25 | 4.6| 9.2 |174 | 1.06 | 1 min.| 388| |780|550|720|750 | 30 | 25 | 8.8|17.6 |174 | 1.06 | 5 min.| 389| |780| |720|750 | 30 | 25 | 4 | 8 |174 | 1.06 | 1 min.|[I]

390| |780| |720|750 | 30 | 25 | 6.4|12.8 |174 | 1.06 | 5 min.|[E]

391| |730| |640|685 | 45 | 15.2 | 3.7| 7.4 |176 | .886| 1 min.| 392| |730|550|640|685 | 45 | 15.2 | 3.9| 7.8 |176 | .886| 5 min.| ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 396|600|680| |400|540 |140 | 3.86| 2 | .45|170 | .432| |[J]

397| |820| |720|770 | 50 | 15.4 |17.2| 3.87|176 | .890| | 398| |750| |640|695 | 55 | 12.6 |15 | 3.37|177 | .874| | 399| |700| |560|630 | 70 | 9 | 9.4| 2.17|177 | .711| | 400| |670| |480|575 | 95 | 6.05| 4.5| 1.12|178 | .579| | 401| |630|550|400|515 |115 | 4.48| 3.5| .75|178 | .483| | 402| |830| |720|775 | 55 | 14.1 |26 | 5.85|177 | .856| | 403| |630| |320|475 |155 | 3.06| 1.5| .30|179 | .358| | 404| |610| | 60|335 |275 | 1.22| .7| .16|180 | .063| | ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+--- 408|600|610| |120|365 |245 | 1.49| .2| .09|180 | .127| |[K]

413| |660| |400|530 |130 | 4.08| 1 | .45|179 | .450| | 415| |710| |560|635 | 75 | 8.46| 1.9| .86|177 | .691| | 416| |750| |640|695 | 55 | 12.6 | 3.2| 1.44|177 | .820| | 417| |800| |720|760 | 40 | 19 | 3.8| 1.71|175 | .964| | 418| |340| |200|274 | 70 | 3.91| .6| .27|177 | .441| | 419|300|380| |280|330 | 50 | 6.6 | 1.2| .54|176 | .614| | 421| |450| |400|425 | 25 | 17 | 3.2| 1.44|173 | .938| | 423| |515| |480|497.5| 17.5| 28.4 | 4 | 1.8 |169 | 1.13 | | 425| |580| |560|570 | 10 | 57 | 5 | 2.25|162 | 1.43 | | 427| |695| |680|687.5| 7.5| 91.7 | 7 | 3.15|155 | 1.67 | | ---+---+---+---+---+-----+-----+------+----+-----+----+------+-------+---

Legend Remarks: [A] = Slack side of belt running on a board to prevent sagging.

[B] = 10" cast-iron pulleys.

[C] = Belt slipped off 4 m. later.

[D] = Continuing.

[E] = Belt slipped off 2 m. later.

[F] = Belt slipped off 3 m. later.

[G] = Belt slipped off 5 m. later.

[H] = After running 5 minutes at _T_ - _t_ = 560.

[I] = Belt sc.r.a.ped.

[J] = 18 r. p. m. 10" cast-iron pulleys.

[K] = 20" cast-iron pulleys. 18 r. p. m.

These experiments, however, are subject to an error arising from the friction of the belt upon the board, the amount of which was not determined. All of the experiments, in fact, are subject to slight errors which were extremely difficult to eliminate or properly allow for, but an effort has been made throughout to obtain results which should approximate as closely as possible to the truth. The sum of the tensions, as determined by measuring scales, was subject only to errors in observation. This part of the apparatus was carefully tested by a horizontal pull of known amount and made to register correctly.

The difference of the tensions _T_ - _t_, as computed from the reading of the scales, was measured by the force of an equivalent moment at 20"

radius. This moment, divided by the radius of the pulley was taken to be the difference _T_ - _t_.

In this calculation, it will be noticed that two slight corrections have been omitted which are opposite in effect and about equal in degree. One is the friction of the brake shaft in its bearings, which of course was not recorded on the scales, and the other is the thickness of the belt which naturally increases the effective radius of the pulley. Both of these errors are somewhat indefinite, but the correctness of the results obtained was tested in a number of cases by the sag of the belt, and the tension _t_, as calculated from the sag, was found to agree closely with the tension calculated by the adopted method.

As the limiting capacity of the belt was reached, the difficulty of obtaining simultaneous and accurate observations was increased by the vibrations of the scale beams. This was apparently due to irregularity in the slip, and it was only by the use of heavily loaded beams and a dash-pot that readings could then be taken at all. The dash-pot consisted of a large flat plate suspended freely in a bucket of water by a fine wire from the scale beam. This provision, however, was applied only to the scales on which the vibrations were more p.r.o.nounced.

TABLE IV.

DOUBLE OAK-TANNED LEATHER BELT 4" WIDE BY 5/16" THICK AND 30 FT. LONG, WEIGHING 17 LBS., ON 10" CAST-IRON PULLEYS. 160 R. P. M.

Legend column headings: [A] = No. of Experi'nt.

[B] = Sum of Tensions. _T_ + _t_ Initial.

[C] = Sum of Tensions. _T_ + _t_ Working.

[D] = Sum of Tensions. _T_ + _t_ Final.

[E] = _T_ - _t_ Working.

[F] = _T_ [G] = _t_ [H] = _T_/_t_ [I] = Percentage of Slip.

[J] = Velocity of Slip in ft. per min.

[K] = Arc of contact.

[L] = Coefficient of Friction.

[M] = Duration of run at time of experiment.

[N] = Remarks.

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- [A]|[B]|[C]|[D]|[E]| [F] | [G] | [H] | [I]| [J] | [K]| [L] | [M] |[N]

---+---+---+---+---+-----+-----+-----+----+-----+----+-----+------+--- 209|120|120| | 48| 84 | 36 | 2.33| .4| .8 |176| .275| | 210| |140| | 80|110 | 30 | 3.67| .6| 1.2 |175 | .426| | 211| |168| |120|144 | 24 | 6 | .9| 1.8 |174 | .590| | 212| |198| |160|179 | 19 | 9.42| 1.6| 3.2 |170 | .756| | 213| |235| |200|217.5| 17.5|12.4 | 2.3| 4.6 |174 | .829| | 214| |270| |240|255 | 15 |17 | 3.2| 6.4 |168 | .966| | 215| |310| |280|295 | 15 |19.7 | 5.1|10.2 |168 |1.02 | |[A]